Type-II Dirac phonons in a two-dimensional phononic crystal

We explore the distinctive properties associated with a type-II Dirac point in a simply structured phononic crystal with a lattice deformation. This type-II Dirac point emerges at the Brillouin zone boundary, resulting from the lifting of two degenerate bands and featuring a conical-like Fermi surface in the equi-frequency curve. A practical implementation of such a phononic crystal is achieved with LEGO bricks. Upon introducing a periodic parity-time (PT) symmetric non-Hermitian perturbation, the phononic crystal undergoes a transition from PT-symmetric phase to PT-broken phase, causing the deformation of type-II Dirac point into an oval of exceptional points in the band structure. Based on the eigenmodes of the type-II Dirac point, a k⃗⋅p⃗ perturbation theory can be used to characterize these systems before and after the phase transition. Using a scattering matrix, we analyze the symmetric and broken phases and demonstrate that broadband unidirectional transparency and a coherent perfect absorber and laser can be realized with such a phononic crystal slab.